6=-16x^2+85x+4

Solution for 6=-16x^2+85x+4 equation:

6=-16x^2+85x+4

We move all terms to the left:

6-(-16x^2+85x+4)=0

We get rid of parentheses

16x^2-85x-4+6=0

We add all the numbers together, and all the variables

16x^2-85x+2=0

a = 16; b = -85; c = +2;
Δ = b2-4ac
Δ = -852-4·16·2
Δ = 7097
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-85)-\sqrt{7097}}{2*16}=\frac{85-\sqrt{7097}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-85)+\sqrt{7097}}{2*16}=\frac{85+\sqrt{7097}}{32}
$